The performance of the neural networks is related to hyperparameters \(\gamma \)  and \(\epsilon \) . Without loss of generality, we take the examples of neural networks with the excess noise \(\xi \)  between \(0.002\)  and \(0.005\)  (Fig. REF ). When \(\gamma =0.20\)  and \(\epsilon =0.80\) , key rates predicted by the neural network are strictly lower than those obtained by the numerical method in Refs. [1]}, [2]}, which means that the key rates predicted by the neural network are information-theoretically secure. Meanwhile, the absolute values of the relative deviations are mainly distributed between \(0.05\)  and \(0.20\)  (Fig. REF a-b). Fig. REF c-f plot the corresponding results for the hyperparameters \(\gamma =0.20\) , \(\epsilon =0.90\)  and \(\gamma =0.80\) , \(\epsilon =0.80\) , respectively. Note that the partial key rates predicted by the neural networks under \(\gamma =0.20\) , \(\epsilon =0.90\)  and \(\gamma =0.80\) , \(\epsilon =0.80\)  are higher than key rates obtained by the numerical method. This indicates that the performance of neural networks trained with hyperparameters \(\gamma =0.20\) , \(\epsilon =0.90\)  and \(\gamma =0.80\) , \(\epsilon =0.80\)  is not as good as that of neural network trained with hyperparameters \(\gamma =0.20\)  and \(\epsilon =0.80\) . Therefore, we need to carefully tune hyperparameters of the neural networks to ensure their stable performance.
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